Saido Berahino struck just before half-time to cancel out an early opener from Diafra Sakho in an entertaining first period, while Aaron Cresswell’s thundering free-kick against the post was a rare highlight in the second.
With Pulis set to take charge of the first team for Saturday’s FA Cup tie with Gateshead, Albion turned in an impressive performance that ended a run of three consecutive defeats, although they have won only one of their last 10 matches.
The visitors were the better team in the early stages, with Stephane Sessegnon in particular pulling the strings in midfield from the outset.
The Benin international had a shot well blocked by James Collins after the first of many incisive, driving runs, while Cresswell stabbed tamely at Ben Foster as West Ham began to atone for a sluggish start.
The Hammers barely got out of their own half in the first 10 minutes, but they still managed to take the lead in the 11th minute as Cresswell whipped in a superb first-time cross from the left for an unmarked Sakho to glance past Foster from close range.
Stewart Downing’s deflected shot was blocked by Foster before the Baggies almost levelled when Youssuf Mulumbu’s cross to the far post was met by a cracking first-time volley from Chris Baird, but Adrian pulled off a smart reaction save to keep his side in front.
Sessegnon scuffed wide and Chris Brunt hooked inches past the upright as Albion continued to press, while James Morrison’s curling effort sailed narrowly over the bar.
But three minutes before the break, West Brom were rewarded for their attacking intent as Sessegnon sauntered down the left from a flowing counter-attack and crossed low for Berahino, who side-footed calmly past Adrian from 10 yards.
Berahino came close to doubling his tally five minutes after the interval, when his shot took a wild deflection off Collins and was beaten away at full stretch by Adrian.
Mulumbu blazed into the side-netting from another neat lay-off by Sessegnon, but it was West Ham who came closest to another goal when Cresswell’s cracking 25-yard free-kick cleared the wall and beat Foster, only for the ball to cannon off the foot of the post.
Matt Jarvis failed to make a decent connection with a near-post centre from Enner Valencia, and Sessegnon dragged another shot wide in the closing stages.
With legs tiring after another hectic festive schedule, Silvestre Varela almost bagged a dramatic winner in added time as his strike from the edge of the box flicked off Collins and shaved the outside of the post with Adrian struggling to reach.
West Ham: Adrian (6), Jenkinson (6), Collins (7), Reid (5), Cresswell (7), Song (5), Amalfitano (5), Kouyate (5), Downing (6), Carroll (5), Sakho (6).
Used subs: Jarvis (5), Valencia (5), Cole (5)
West Brom: Foster (6), Wisdom (6), McAuley (6), Lescott (6), Baird (6), Mulumbu (6), Brunt (6), Dorrans (6), Sessegnon (8), Morrison (6), Berahino (7).
Used subs: Yacob (5), Varela (6), Ideye (5)
Man of the match: Stephane Sessegnon.